Proof by Induction
by Phoenix Boy
Summary: Niou has strange hobbies.


Niou titled his piece of paper and underlined it. It was all very well to be solving simultaneous equations in class but there was no buzz of satisfaction on completion, no feeling of a job well done. This was the real stuff. Proper maths.

The Tennis Club Will All Pass Maths: A Proof by Induction.

Besides, he'd finished and checked his homework, and now had time to kill in the library before training. It wasn't like there was much else to do, not with Yanagi there to keep an eye on them. Slipping one past their strategist took a lot more forward planning.

_In the case n=1_ Niou wrote and paused. Statements had to be indisputably true for this to work. _I am in the tennis club and I will pass maths since my coursework already takes me over the lower threshold. Hence the statement holds for n=1._

"Niou-senpai, what're you doing?" Kirihara asked. Surely he couldn't be bored already? Lessons had only just ended. Where were Marui and his bottomless supply of gum when you needed them? Yanagi wasn't any help – he could study through a riot, if he chose.

"Nothing you'd understand," Niou said, pen hovering over the next line. That was another true statement – Kirihara still had problems factorising, there was no way he'd follow this. Yanagi finished his page and looked over at Niou's working.

_Assume the case n=k for some integer k,_ Niou wrote - k had to be an integer because half a tennis club member wouldn't be sitting the exam. No thinking involved there. _Thus k members will all pass the exam._

The tennis club were taking maths very seriously this term. Those k members would form a study group and make sure they passed.

_For the case n=k+1, the k members invite the (k+1)th member to the study group and as a result he will pass the exam._ That member would pass the exam or else, the others would see to that. _The hypothesis holds for n=k+1 if it holds for n=k and it holds for n=1, hence it is true for all members of the club._

"What happens if the element n=1 isn't you – it's a random selection, isn't it? Then the inductive step doesn't hold," Yanagi said. Niou looked at it. He was probably right – Yanagi had an annoying habit of usually being correct and besides, tennis players were much harder to get to conform than abstract elements. It would be much easier if Kirihara were sitting the same exam as the rest of them or if Sanada were sitting the same one as Kirihara.

"Hah! Who doesn't understand it?" Kirihara said and grabbed the paper. He began to read it, tracing each line with his finger, eyebrows dipping closer and closer together. Niou tore a new sheet out of his notebook and grinned. He'd see what Yanagi did with this one.

The Tennis Club Will All Pass Maths: A Proof by Intimidation.

_The tennis club members will all pass maths – this result is obvious._

"Proof by intimidation?"

"It was on a website somewhere. Prove me wrong if you think you can."

Yanagi laughed. No wonder. This way would work – Yanagi wouldn't bother trying – but Niou really should be able to come up with something more convincing.

Niou absently handed Yanagi that page and scrawled a line at the top of a third. Proof by Intimidation: Alternative Method. He just had to make sure Sanada didn't see this one. Yanagi would appreciate it, though.

_Assume that all tennis club members plan to remain tennis club members. Assume also that all tennis club members have a certain level of common sense._

Niou hesitated. That assumption was a bit dubious. Still, most of them could at least manage self-preservation.

_Failing maths = suspension from club activities._

_Suspension from club activities = angry Yukimura = strikemillions/strike thousands of laps = insanity_

_This is a contradiction. Hence, all tennis club members will pass maths._

"Niou!" Yukimura said quietly behind him. Niou pulled his notebook hastily over his most recent proof and twisted in his chair. Yukimura looked pained. A moment's consideration: yes, Yukimura probably had just come from a maths lesson. "Tonight, after training, I'd like you to run tutoring for all the regulars. We have to pass the test on Friday if we want to accompany Sato to the Newcomers' Tournament this weekend."

Tonight... well, he'd already agreed to help Marui, it wouldn't be much harder to give Sanada a hand as well. The others could bugger off and do their own homework. It wasn't like any of them were struggling.

It was more than his life was worth if Sanada failed maths.


End file.
